How can I decimate a mesh to remove unnecessary triangles?
If decimate is too destructive, then while in edit mode, select all, then press X>limited dissolve to remove excess edges in your model. You can adjust the angle threshold in the operator panel as needed. Don't forget to also remove doubles with W>remove doubles. 



You can also try tris to quads. Press Spaebar and type in tris to quads, and select the operation from the menu, or or press Alt + J